Paratellurite ($\alpha$–TeO2) Structure : A2B_tP12_92_b_a
| Prototype | : | O2Te |
| AFLOW prototype label | : | A2B_tP12_92_b_a |
| Strukturbericht designation | : | None |
| Pearson symbol | : | tP12 |
| Space group number | : | 92 |
| Space group symbol | : | $P4_{1}2_{1}2$ |
| AFLOW prototype command | : | aflow --proto=A2B_tP12_92_b_a --params=$a$,$c/a$,$x_{1}$,$x_{2}$,$y_{2}$,$z_{2}$ |
- Although this as the same space group and Wyckoff positions as $\alpha$–cristobalite ($C30$), the actual positions of the atoms are substantially different, so we have given the two compounds separate entries in the encyclopedia.
Simple Tetragonal primitive vectors:
\[ \begin{array}{ccc} \mathbf{a}_1 & = & a \, \mathbf{\hat{x}} \\ \mathbf{a}_2 & = & a \, \mathbf{\hat{y}} \\ \mathbf{a}_3 & = & c \, \mathbf{\hat{z}} \\ \end{array} \]
Basis vectors:
\[ \begin{array}{ccccccc} & & \text{Lattice Coordinates} & & \text{Cartesian Coordinates} &\text{Wyckoff Position} & \text{Atom Type} \\ \mathbf{B}_{1} & = & x_{1} \, \mathbf{a}_{1} + x_{1} \, \mathbf{a}_{2} & = & x_{1}a \, \mathbf{\hat{x}} + x_{1}a \, \mathbf{\hat{y}} & \left(4a\right) & \text{Te} \\ \mathbf{B}_{2} & = & -x_{1} \, \mathbf{a}_{1}-x_{1} \, \mathbf{a}_{2} + \frac{1}{2} \, \mathbf{a}_{3} & = & -x_{1}a \, \mathbf{\hat{x}}-x_{1}a \, \mathbf{\hat{y}} + \frac{1}{2}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Te} \\ \mathbf{B}_{3} & = & \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{2} + \frac{1}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{y}} + \frac{1}{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Te} \\ \mathbf{B}_{4} & = & \left(\frac{1}{2} +x_{1}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{1}\right) \, \mathbf{a}_{2} + \frac{3}{4} \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{1}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{1}\right)a \, \mathbf{\hat{y}} + \frac{3}{4}c \, \mathbf{\hat{z}} & \left(4a\right) & \text{Te} \\ \mathbf{B}_{5} & = & x_{2} \, \mathbf{a}_{1} + y_{2} \, \mathbf{a}_{2} + z_{2} \, \mathbf{a}_{3} & = & x_{2}a \, \mathbf{\hat{x}} + y_{2}a \, \mathbf{\hat{y}} + z_{2}c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O} \\ \mathbf{B}_{6} & = & -x_{2} \, \mathbf{a}_{1}-y_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} +z_{2}\right) \, \mathbf{a}_{3} & = & -x_{2}a \, \mathbf{\hat{x}}-y_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O} \\ \mathbf{B}_{7} & = & \left(\frac{1}{2} - y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O} \\ \mathbf{B}_{8} & = & \left(\frac{1}{2} +y_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} +z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{3}{4} +z_{2}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O} \\ \mathbf{B}_{9} & = & \left(\frac{1}{2} - x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} +y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{1}{4} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2}-x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2} +y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{1}{4}-z_{2}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O} \\ \mathbf{B}_{10} & = & \left(\frac{1}{2} +x_{2}\right) \, \mathbf{a}_{1} + \left(\frac{1}{2} - y_{2}\right) \, \mathbf{a}_{2} + \left(\frac{3}{4} - z_{2}\right) \, \mathbf{a}_{3} & = & \left(\frac{1}{2} +x_{2}\right)a \, \mathbf{\hat{x}} + \left(\frac{1}{2}-y_{2}\right)a \, \mathbf{\hat{y}} + \left(\frac{3}{4}-z_{2}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O} \\ \mathbf{B}_{11} & = & y_{2} \, \mathbf{a}_{1} + x_{2} \, \mathbf{a}_{2}-z_{2} \, \mathbf{a}_{3} & = & y_{2}a \, \mathbf{\hat{x}} + x_{2}a \, \mathbf{\hat{y}}-z_{2}c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O} \\ \mathbf{B}_{12} & = & -y_{2} \, \mathbf{a}_{1}-x_{2} \, \mathbf{a}_{2} + \left(\frac{1}{2} - z_{2}\right) \, \mathbf{a}_{3} & = & -y_{2}a \, \mathbf{\hat{x}}-x_{2}a \, \mathbf{\hat{y}} + \left(\frac{1}{2}-z_{2}\right)c \, \mathbf{\hat{z}} & \left(8b\right) & \text{O} \\ \end{array} \]References
- P. A. Thomas, The crystal structure and absolute optical chirality of paratellurite, $\alpha$–TeO2, J. Phys. C:\ Solid State Phys. 21, 4611–4627 (1988), doi:10.1088/0022-3719/21/25/009.
Found in
- M. Ceriotti, F. Pietrucci, and M. Bernasconi, Ab initio study of the vibrational properties of crystalline TeO2: The $\alpha$, $\beta$, and $\gamma$ phases, Phys. Rev. B 73, 104304 (2006), doi:10.1103/PhysRevB.73.104304.